Class 10

Math

All topics

Sequences and Series

Find the sum of first $22$ terms of an AP in which $d=7$ and $22_{nd}$ term is $149$.

Given $d=7,a_{22}=149$

We want to find $S_{22}.$

$a_{n}=a+(n−1)d$

$⇒a_{22}=a+(22−1)7$

$⇒149=a+(21)(7)$

$⇒149=a+147$

$∴a=2$

We have $S_{n}=2n (a+a_{n})$ then

$S_{22}=222 (2+149)$

$=11×151$

$=1661$